## Abstract

In this work, natural convection fin experiments are performed with mild steel as the fin and an aluminium plate as base. The dimension of the mild steel fin is 250 mm × 150 mm × 6 mm and the aluminium base plate is 250 mm × 150 mm × 8 mm. A heater is provided on one side of the aluminium base plate and the mild steel fin emerges on the other side of the plate. The heater provides required heat flux to the fin base; several steady-state natural convection experiments are performed for different heat fluxes and corresponding temperature distributions are recorded using thermocouples at different locations of the fin. In addition, a numerical model is developed that contains the dimensions of the fin set-up along with extended domain to capture the information of the fluid. Air is treated as a working fluid that enters the extended domain and absorbs heat from the heated fin. The temperature and the velocity of the fluid in the extended domain are obtained by solving the Navier–Stokes equation. The numerical model is now treated as a forward model that provides the temperature distribution of the fin for a given heat flux. An inverse problem is proposed to determine the heat flux that leads to the temperature distributions during experiments. The temperature distributions of the experiments and forward model are compared to identify the unknown heat flux. In order to reduce computational cost of the inverse problem the forward model is then replaced with artificial neural network (ANN) as data reduction, which is developed using several computational fluid dynamics solutions, and the inverse estimation is accomplished. The results indicate that a quick solution can be obtained using ANN with a limited number of experiments.

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## References

- 1
Beck J V, Blackwell B and Clair Jr C R S 1985

*Inverse heat conduction: ill-posed problems.*USA: Wiley-Interscience Publication - 2
Ozisik M N and Orlande H R B 2000

*Inverse Heat Transfer: Fundamentals and Applications*Boca Raton: CRC Press - 3
Cui M, Yang K, Xu X L, Wang S D and Gao X W 2016 A modified Levenberg–Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems.

*Int. J. Heat Mass Transf.*97: 908–916 - 4
Dantas L B, Orlande H R B and Cotta R M 2003 An inverse problem of parameter estimation for heat and mass transfer in capillary porous media.

*Int. J. Heat Mass Transf.*46: 1587–1596 - 5
Huang C H and Wang S P 1999 A three-dimensional inverse heat conduction problem in estimating surface heat flux by conjugate gradient method.

*Int. J. Heat Mass Transf.*42: 3387–3403 - 6
Huang C H and Chen W C 2000 A three-dimensional inverse forced convection problem in estimating surface heat flux by conjugate gradient method.

*Int. J. Heat Mass Transf.*43: 3171–3181 - 7
Mohammadiun M, Rahimi A B and Khazaee I 2011 Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method.

*Int. J. Therm. Sci.*50: 2443–2450 - 8
Mohebbi F and Sellier M 2016 Estimation of thermal conductivity, heat transfer coefficient, and heat flux using a three dimensional inverse analysis.

*Int. J. Therm. Sci.*99: 258–270 - 9
De Faoite D, Browne D J, Gamboa J D and Stanton K T 2014 Inverse estimate of heat flux on a plasma discharge tube to steady-state conditions using thermocouple data and a radiation boundary condition.

*Int. J. Heat Mass Transf.*77: 564–576 - 10
Dumek V, Druckmuller M, Raudensky M and Woodburg K A 1993 Novel approaches to the IHCP: neural networks and expert systems. In:

*Proceedings of the International Conference on Inverse Problems in Engineering: Theory and Practice*, ASME, New York, USA, pp. 275–282 - 11
Jambunathan K, Hartle S L, Ashforth-Frost S and Fontama V N 1996 Evaluating convective heat transfer coefficients using neural networks.

*Int. J. Heat Mass Transf.*39: 2329–2332 - 12
Sablani S S 2004 A neural network approach for non-iterative calculation of heat transfer coefficient in fluid-particle systems.

*Chem. Eng. Process.*40: 363–369 - 13
Diaz G, Sen M, Yang K T and McClain R L 2001 Dynamic prediction and control of heat exchangers using artificial neural networks.

*Int. J. Heat Mass Transf.*44: 1671–1679 - 14
Kumar H and Gnanasekaran N 2018 A Bayesian inference approach: estimation of heat flux from fin for perturbed temperature data.

*Sadhana Acad. Proc. Eng. Sci.*43: 62 - 15
Krejsa J, Woodbury K A, Ratliff J D and Raudensky M 1999 Assessment of strategies and potential for neural networks in the inverse heat conduction problem.

*Inverse Probl. Sci. Eng.*7: 197–213 - 16
Shiguemori E H, Da Silva J D and de Campos Velho H F 2004 Estimation of initial condition in heat conduction by neural network.

*Inverse. Probl. Sci. Eng.*12: 317–328 - 17
Ghosh S, Pratihar D K, Maiti B and Das P K 2011 Inverse estimation of location of internal heat source in conduction.

*Inverse. Probl. Sci. Eng.*19: 337–361 - 18
Ermis K, Erek A and Dincer I 2007 Heat transfer analysis of phase change process in a finned-tube thermal energy storage system using artificial neural network.

*Int. J. Heat Mass Transf.*50: 3163–3175 - 19
Sablani S S, Kacimov A, Perret J, Mujumdar A S and Campo A 2005 Non-iterative estimation of heat transfer coefficients using artificial neural network models.

*Int. J. Heat Mass Transf.*48: 665–679 - 20
Guanghui S, Morita K, Fukuda K, Pidduck M, Dounan J and Miettinen J 2003 Analysis of the critical heat flux in round vertical tubes under low pressure and flow oscillation conditions. Applications of artificial neural network.

*Nucl. Eng. Des.*220: 17–35 - 21
Balaji C and Padhi T 2010 A new ANN driven MCMC method for multi-parameter estimation in two-dimensional conduction with heat generation.

*Int. J. Heat Mass Transf.*53: 5440–5455 - 22
Deng S and Hwang Y 2006 Applying neural networks to the solution of forward and inverse heat conduction problems.

*Int. J. Heat Mass Transf.*49: 4732–4750 - 23
Ben-Nakhi A, Mahmoud M A and Mahmoud A M 2008 Inter-model comparison of CFD and neural network analysis of natural convection heat transfer in a partitioned enclosure.

*Appl. Math. Modell.*32: 1834–1847 - 24
Wang H, Yang Q, Zhu X, Zhou P and Yang K 2018 Inverse estimation of heat flux using linear artificial neural networks.

*Int. J. Therm. Sci.*132: 478-485 - 25
Czel B, Woodbury K A and Grof G 2014 Simultaneous estimation of temperature-dependent volumetric heat capacity and thermal conductivity functions via neural networks.

*Int. J. Heat Mass Transf.*68: 1–3 - 26
Romero-Mendez R, Lara-Vazquez P, Oviedo-Tolentino F, Durn-Garcia H M, Perez-Gutierrez F G and Pacheco-Vega 2016 Use of artificial neural networks for prediction of the convective heat transfer coefficient in evaporative mini-tubes.

*Ing. Investig. Tecnol.*17: 23–34 - 27
Kumar M K, Vishweshwara P S, Gnanasekaran N and Balaji C 2018 A combined ANN-GA and experimental based technique for the estimation of the unknown heat flux for a conjugate heat transfer problem.

*Heat Mass Transf.*54: 3185–3197 - 28
Gnanasekaran N and Balaji C 2011 A Bayesian approach for the simultaneous estimation of surface heat transfer coefficient and thermal conductivity from steady state experiments on fins.

*Int. J. Heat Mass Transf.*54: 3060–3068 - 29
Reddy B K, Gnanasekaran N and Balaji C 2012 Estimation of thermo-physical and transport properties with Bayesian inference using transient liquid crystal thermography experiments.

*J. Phys. Conf. Ser.*395: 012082 - 30
Vishweshwara P S, Harsha Kumar M K, Gnanasekaran N and Arun M 2019 3D coupled conduction–convection problem using in-house heat transfer experiments in conjunction with hybrid inverse approach.

*Eng. Comput*36: 3180–3207

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Kumar, M.K.H., Vishweshwara, P.S. & Gnanasekaran, N. Evaluation of artificial neural network in data reduction for a natural convection conjugate heat transfer problem in an inverse approach: experiments combined with CFD solutions.
*Sādhanā* **45, **78 (2020). https://doi.org/10.1007/s12046-020-1303-x

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### Keywords

- Heat transfer
- natural convection
- fin
- ANN
- forward model
- inverse
- estimation